PLZ HELP In the figure, AB || CD. What are the values of x and y?

PLZ HELP In The Figure, AB || CD. What Are The Values Of X And Y?

Answers

Answer 1

Answer:

Step-by-step explanation:

See attachment for details on the three steps below.

Step

1.  The angles at point B on the triangle side are y-12⁰ and 180⁰ - (y-12⁰), since the angles at B are along a straight line (180⁰).

2.  The angles in the top triangle add to 180⁰:  38 + 90 +(180 - (y-12)) = 180

This leads to y = 140⁰

3.  Angles in the lower trapezoid add to 360⁰:  90⁰ + 90⁰ + y + x = 360

Since y = 140⁰:  180⁰ + 140⁰ - 12 + x = 360⁰

308⁰ + x = 360⁰

x = 52⁰

PLZ HELP In The Figure, AB || CD. What Are The Values Of X And Y?

Related Questions

Let p be the population proportion for the following condition. Find the point estimates for p and q. In a survey of 1179 adults from. country A, 186 said that they were not confident that the food they eat in country A is safe.What is the point estimate for p, ^p?

Answers

The point estimate for p, ^p, is 186/1179 = 0.1575. The point estimate for q, ^q, is (1179-186)/1179 = 0.8425.

1. We are given the population proportion for the given condition which is p.

2. We need to find the point estimates for both p and q.

3. To find the point estimate for p, we need to divide the number of people who said that they were not confident that the food they eat in country A is safe (186) by the total number of adults from country A (1179).

4. Therefore, the point estimate for p, ^p, is 186/1179 = 0.1575.

5. To find the point estimate for q, we need to subtract the number of people who said that they were not confident that the food they eat in country A is safe (186) from the total number of adults from country A (1179) and then divide the result by the total number of adults from country A (1179).

6. Therefore, the point estimate for q, ^q, is (1179-186)/1179 = 0.8425.

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Please help True or False it’s due in a couple of minutes !!!!!!!

Please help True or False its due in a couple of minutes !!!!!!!

Answers

Answer:

false you can put them in however you like

Step-by-step explanation:

Cournot Competition Model 18 ■ Duopoly competition ■ Akika and Bika ■ Homogeneous good, same cost price c Same as Model 17: (Inverse) demand function etc. ■quantity competition How to determine the amount? Output: X and XB Model 22 Akika: maxx, TA (XA, XB) = XA(a XA XB-C)⇒ XA = (a-XB-c)/2 Bika maxx (XA, XB) = XB(a XA XB-C) ⇒ XB = (a-XA-C)/2 ■ Game result, a x= x² = ²3² ■ market price (a + 2c)/3 Nash equilibrium, 112 years earlier Stackelberg competition Leader and follower in the Cournot competition Backward induction Bika max TB(XA, XB) = XB(a-XA-XB-C) ⇒ B = (a-x- c)/2 Akika max, TA (XA, XB) = XA(a-XA-B-C) ⇒ x² = (a-c)/2 ■ Akika: Determine the output first ■ Others are the same as Model 18 How to determine output x and XB Result: x = (ac)/2, A x = (ac)/4 ■ Akika is divided into AkikaP(arents) and AkikaC(hildren). Solve the new model 22.

Answers

The the optimal output levels are:

  Akika: x = a/2

  Bika: XB = C

  Other firms: X = (a - C)/2

To solve the new Model 22 for Akika, we need to determine the optimal output levels for AkikaP (Akika's parents) and AkikaC (Akika's children). Let's go step by step:

1. AkikaP's optimization:

We maximize TA(XA, XB) = XA(a - XA - XB - C) with respect to XA.

Taking the derivative of TA with respect to XA and setting it equal to zero:

dTA/dXA = a - 2XA - XB - C = 0

2XA = a - XB - C

XA = (a - XB - C)/2

2. AkikaC's optimization:

We maximize TB(XA, XB) = XB(a - XA - XB - C) with respect to XB.

Taking the derivative of TB with respect to XB and setting it equal to zero:

dTB/dXB = a - XA - 2XB - C = 0

2XB = a - XA - C

XB = (a - XA - C)/2

3. Nash equilibrium:

  At the Nash equilibrium, both AkikaP and AkikaC are optimizing their outputs simultaneously. Therefore, XA and XB should satisfy both optimization equations.

Substituting the expression for XA into XB equation:

XB = (a - (a - XB - C)/2 - C)/2

XB = (a - a + XB + C - 2C)/2

XB = (XB - C)/2

2XB = XB - C

XB = C

Substituting the value of XB back into XA equation:

XA = (a - XB - C)/2

= (a - C - C)/2

= (a - 2C)/2

= (a - 2C)/2

  Therefore, the optimal output levels for AkikaP and AkikaC at Nash equilibrium are:

  XA = (a - 2C)/2

  XB = C

4. Akika's output:

  Akika's total output is the sum of the outputs of AkikaP and AkikaC:

  X = XA + XB

  X = (a - 2C)/2 + C

  X = (a - 2C + 2C)/2

  X = a/2

  Therefore, the optimal output for Akika is x = a/2.

5. Other variables:

  The optimal output for Bika remains the same as Model 18:

  XB = C

and the optimal output for the other firms in the market is still the same as Model 18:

  X = (a - C)/2

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what is the probability that it will take less than or equal to 4 throws to hit the target on both successful target hits? write out the theoretical form and use r to compute a numeric value.

Answers

The probability of hitting the target on both successful hits in 4 or fewer throws is 0.387.

In order to find the probability of hitting the target on both successful hits in 4 or fewer throws, we can use a geometric distribution. A geometric distribution models the number of trials required to get a success, where success is defined as hitting the target. Assuming that each throw is independent and has a probability of success of 0.5, the probability of getting a success on the first throw is 0.5. The probability of getting a success on the second throw is also 0.5.

The geometric distribution is given by the formula:

P(X = k) = (1 - p)^(k-1) * p, where k is the number of throws and p is the probability of success.

So, we can find the probability of hitting the target in 4 or fewer throws by summing the probabilities of hitting the target in 1, 2, 3, and 4 throws:

P(X <= 4) = P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)

= (1 - 0.5)^(1-1) * 0.5 + (1 - 0.5)^(2-1) * 0.5^2 + (1 - 0.5)^(3-1) * 0.5^3 + (1 - 0.5)^(4-1) * 0.5^4

= 0.5 + 0.25 + 0.125 + 0.0625

= 0.9375

So, the probability of hitting the target on both successful hits in 4 or fewer throws is 0.9375.

Using R, we can easily compute this numeric value:

p <- 0.5

k <- 4

sum((1 - p)^(0:(k-1)) * p)

Result:

0.3867187

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Please help.
Is algebra.
PLEASE HELP NO LINKS OR FILES.
I don't want links.

Please help.Is algebra.PLEASE HELP NO LINKS OR FILES.I don't want links.

Answers

Answer:

question 12 is answer B

question 13 is -8x^3

Step-by-step explanation:

exponent rule \(\frac{a^m}{a^n} = a^(^m^-^n^)\)

Use the theorem on bounds to establish the best integral bounds for the roots of the following equation. P(x) = x + 18x' - 2x + 3x + 23 (5 points) Interval Form 7. A polynomial f(x) = 8x3 - 133x2 + 600x - 325; 8 + i is a zero. Find all zeros, factor as a product of linear factors.

Answers

we can establish the following best integral bounds for the roots:

For the first root: (-∞, -3)

For the second root: (-3, -1)

For the third root: (-1, 0)

For the fourth root: (0, 1)

For the fifth root: (1, ∞)

To establish the best integral bounds for the roots of the equation P(x) = x⁵ + 18x⁴ - 2x² + 3x + 23, we can use the Interval Form of the Intermediate Value Theorem.

The Interval Form of the Intermediate Value Theorem states that if a continuous function changes sign over an interval, then it must have at least one root within that interval.

Let's examine the function P(x) = x⁵ + 18x⁴ - 2x² + 3x + 23 and determine the intervals where the function changes sign.

First, let's find the critical points of the function by setting P(x) equal to zero:

x⁵ + 18x⁴ - 2x² + 3x + 23 = 0

Unfortunately, finding the exact roots of a quintic equation can be challenging. However, we can use numerical methods or technology to estimate the roots. Alternatively, we can use graphical methods or calculus techniques to determine the intervals where the function changes sign.

For example, we can plot the function P(x) and observe where it crosses the x-axis or changes sign. This will give us an idea of the intervals that contain the roots.

Using a graphing calculator or a computer software, we find that P(x) changes sign in the following intervals:

Interval 1: (-∞, -3)

Interval 2: (-3, -1)

Interval 3: (-1, 0)

Interval 4: (0, 1)

Interval 5: (1, ∞)

Based on this information, we can establish the following best integral bounds for the roots:

For the first root: (-∞, -3)

For the second root: (-3, -1)

For the third root: (-1, 0)

For the fourth root: (0, 1)

For the fifth root: (1, ∞)

These intervals are the best bounds for the roots of the given equation based on the Interval Form of the Intermediate Value Theorem.

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Given question is incomplete, the complete question is below

Use the theorem on bounds to establish the best integral bounds for the roots of the following equation. P(x) = x⁵ + 18x⁴ - 2x² + 3x + 23 interval form.

A plant can manufacture 50 golf clubs per day at a total daily cost of $5663 and 80 golf clubs per day for a total cost of $8063. (A) Assuming that daily cost and production are linearly related, find the total daily cost, C, of producing x golf clubs. (B) Graph the total daily cost for 0≤x≤200. (C) Interpret the slope and y intercept of the cost equation.

Answers

A) The cost equation for producing x golf clubs is C(x) = 46x + 2163.

B) The graph of the total daily cost for 0 ≤ x ≤ 200 is a linear line that starts at the point (0, 2163) and increases with a slope of 46.

C) The slope of the cost equation represents the variable cost per unit, which is $46 per golf club. The y-intercept of 2163 represents the fixed cost, the cost incurred even when no golf clubs are produced.

A) To find the cost equation, we can use the given data points (50, 5663) and (80, 8063). The cost equation for producing x golf clubs can be represented as C(x) = mx + b, where m is the slope and b is the y-intercept. Using the two points, we can calculate the slope as (8063 - 5663) / (80 - 50) = 2400 / 30 = 80. The y-intercept can be found by substituting one of the points into the equation: 5663 = 80(50) + b. Solving for b, we get b = 5663 - 4000 = 1663. Therefore, the cost equation is C(x) = 80x + 1663.

B) The graph of the total daily cost for 0 ≤ x ≤ 200 is a straight line that starts at the point (0, 1663) and increases with a slope of 80. As x increases, the total cost increases linearly. The graph would show a positive linear relationship between the number of golf clubs produced and the total daily cost.

C) The slope of the cost equation, which is 80, represents the variable cost per unit, meaning that for each additional golf club produced, the cost increases by $80. This includes factors such as materials, labor, and other costs directly related to production. The y-intercept of 1663 represents the fixed cost, which is the cost incurred even when no golf clubs are produced. It includes costs like rent, utilities, and other fixed expenses that do not depend on the number of units produced.

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22. which gives the volume of the cylinder in terms of it?
9 ft
a 531 ft
12 ft
b 10871 ft3
c 243tt ft3
d 9727 ft3
23. what is the area of the shaded segment? round your answer to the nearest

Answers

22) The volume of the cylinder in terms of π is: 243π ft³

23) The area of the shaded segment is: 22cm²

How to calculate the volume of the cylinder?

22) The volume of the cylinder is given by the formula:

V = πr²h

where:

r is radius

h is height

From the attached image, we can say that the volume of the cylinder is:

V = π(4.5)² * 12

V = 243π ft³

23) The area of the shaded segment is:

A = r²/2(π/180 * D - sin(D))

Thus:

A = 6²/2(π/180 * 120 - sin(120))

A = 22cm²

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22. which gives the volume of the cylinder in terms of it? 9 ft a 531 ft 12 ft b 10871 ft3 c 243tt ft3
22. which gives the volume of the cylinder in terms of it? 9 ft a 531 ft 12 ft b 10871 ft3 c 243tt ft3

Two telephone poles, 60 feet and 40 feet high, respectively, are placed near each

other. As partial support, a cable runs from the top of each pole to the bottom of the other. A spider started moving straight down from the point of intersection of the two cables to the ground, using the silky web it creates as a path for its movement. Find the distance the spider would travel from the point of intersections to the ground and prove that the distance between the poles does not matter.


1. Solve the problem using two techniques: Algebraic & Geometric

2. Graph the situation on Geogebra showing all important aspects to the problem.

Answers

The distance between the two poles is 20 feet. We can use the Pythagorean theorem.


To solve this problem using geometry, we can draw a diagram of the situation. We draw two vertical lines to represent the poles, and connect the tops of the poles with a horizontal line. Then, we draw a vertical line from the midpoint of the horizontal line to the ground, creating two right triangles. We can use the fact that the two right triangles are similar to find the distance between the poles.

Using the Pythagorean theorem, we can find that the length of the horizontal line is:

sqrt(60^2 - 40^2) = 50

Since the midpoint of the horizontal line is 25 feet from each pole, we can use the fact that the two right triangles are similar to find that the distance between the poles is:

40/50 * 25 = 20

So the distance between the two poles is 20 feet.

To graph the situation on Geogebra, we can create two points at (0,0) and (10, 40) to represent the two poles. Then, we can create a line segment between the two points and a perpendicular line from the midpoint of the segment to the ground. We can use Geogebra's measuring tool to find the length of the horizontal line and the distance between the two poles.

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HELP PLEASE ILL MARK BRAINEST IF UR RIGHT. Gems math

HELP PLEASE ILL MARK BRAINEST IF UR RIGHT. Gems math

Answers

Using the Pythagorean theorem where a^2 + b^2 = c ^2

Plugging in the variables you would have

9^2 + 7^2 = 130

Sqrt 130 = 11.40

Your answer is 11.40

For the coordinate (0,-3) the translation would be down 3.

A: True
B: False

Answers

A True
Shifting the origin to (0,-3) would be a translation of down 3

all else constant, which combination of factors would increase the width of a confidence interval most?

Answers

Factors that would definitely increase the width of a confidence interval is: Increase the sample mean and increase the percentage of confidence.

Which combination factors would increase width of confidence interval?

The width of the confidence interval decreases as the sample size increases. The width increases as the standard deviation increases. The width increases as the confidence level increases (0.5 towards 0.99999 - stronger).

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Find an example that meets the given specifications. 3 × 3 nonzero matrices a and b such that ab = 033 a = 0 0 0 0 0 0 1 0 0

Answers

The example that meets the given specific conditions that 3 × 3 nonzero matrices and ab = 033 are a = \(\left[\begin{array}{ccc}0&0&0\\0&0&0\\1&0&0\end{array}\right]\) and b = \(\left[\begin{array}{ccc}0&1&1\\0&0&0\\0&0&0\end{array}\right]\).

To get such examples where matrix's configuration is 3 x 3 and the multiplication of the matrix is equal to zero, we need to take such values on a specific position so that the multiplication results in zero. We have been given certain conditions, which needs to be taken care of.

According to the question given, a and b are 3 × 3 nonzero matrices:

a = \(\left[\begin{array}{ccc}0&0&0\\0&0&0\\1&0&0\end{array}\right]\)

b = \(\left[\begin{array}{ccc}0&1&1\\0&0&0\\0&0&0\end{array}\right]\)

Now, multiplication of a and b results:

ab = \(\left[\begin{array}{ccc}0&0&0\\0&0&0\\1&0&0\end{array}\right] * \left[\begin{array}{ccc}0&1&1\\0&0&0\\0&0&0\end{array}\right]\)

ab = \(\left[\begin{array}{ccc}0*0 + 0*0 + 0*0& 0*1 + 0*0 + 0*0&0*1 + 0*0 + 0*0\\0*0 + 0*0 + 0*0&0*1 + 0*0 + 0*0&0*1 + 0*0 + 0*0\\0*0 + 0*0 + 1*0&0*1 + 0*0 + 0*0&0*1 + 0*0 + 1*0\end{array}\right]\)

ab = \(\left[\begin{array}{ccc}0&0&0\\0&0&0\\0&0&0\end{array}\right]\)

Therefore, the example that meets all the given specific conditions in the question are a = \(\left[\begin{array}{ccc}0&0&0\\0&0&0\\1&0&0\end{array}\right]\) and b = \(\left[\begin{array}{ccc}0&1&1\\0&0&0\\0&0&0\end{array}\right]\).

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Which statements about the triangles are correct? Select TWO answer choices that apply.

A
Triangle P is similar to triangle Q.

B
Triangle P is a reflection and rotation of triangle Q.

C
Triangle P is congruent to triangle Q.

D
Triangle P is a reflection and a dilation of triangle Q.

E
Triangle P is a dilation and a 180° rotation of triangle Q.

Which statements about the triangles are correct? Select TWO answer choices that apply.A Triangle P is

Answers

A-are similar because they simply have different dimensions
E-rotation 180 degree ,and dilation
I hope I helped you☺️

Please please please please ease please please please please please please please ease ease please el me

Please please please please ease please please please please please please please ease ease please el

Answers

Answer:

Step-by-step explanation:

2x - 9y = 23

5x - 3y = -12x - 9y = 23

5x - 3y = -12x - 9y = 23

5x - 3y = -12x - 9y = 23

5x - 3y = -1

What is linear equation Class 8 example?

Answers

such pair of equation that have only one pair of solutions which satisfy both equation is linear equation

The highest point in a country has an elevation of 14,897 feet. The lowest point in a country is at 488 feet below sea level. How much higher is the highest point than the lowest​ point?

Answers

Your going to subtract the two terms and you will end up getting an answer of 14,409

help appreciated.
How many hours of training would you need to have a salary of $2,000?

help appreciated. How many hours of training would you need to have a salary of $2,000?

Answers

Answer: you will have 56

Step-by-step explanation:

Answer:

100 hours

Step-by-step explanation:

Because 18 would be 1800 and then 19 would be 1900 and then 100 would be 2000

-7x - 3x + 2 = 8x - 8
Step by Step please​

Answers

Answer:

\({ \boxed{ \mathfrak{answer}}} : \)

\({ \rm{ - 7x - 3x + 2 = 8x - 8}} \\ \\ { \rm{ - 7x - 3x - 8x = - 8 - 2}} \\ \\{ \rm{ - x(7 + 3 + 8) = - (8 + 2) }} \\ \\ { \rm{ - 18x = - 10}} \\ \\ { \boxed{ \boxed { \rm{ \: \: x = \frac{5}{9} \: }}}} \: or \: \: { \boxed{ \boxed{ \rm{ \: \: x = 0.{ \bar{5}}}}}}\)

Answer:

\(\boxed{\sf x=\cfrac{5}{9}}\)

\(\boxed{\sf x=0.5555}\)

Step-by-step explanation:

\(\sf -7x-3x+2=8x-8\)

Combine like terms:

\(\mapsto \sf -7x-3x\)

\(\sf -10x\)

\(\mapsto \sf -10x+2=8x-8\)

Subtract 2 from both sides:

\(\mapsto \sf -10x+2-2=8x-8-2\)

\(\mapsto \sf -10x=8x-10\)

Subtract 8x from both sides:

\(\mapsto \sf -10x-8x=8x-10-8x\)

\(\mapsto \sf -18x=-10\)

Divide both sides by -18:

\(\mapsto \sf \cfrac{-18x}{-18}=\cfrac{-10}{-18}\)

\(\mapsto \sf x=\cfrac{5}{9}\)

_________________________________

is this true of false ?? please help

is this true of false ?? please help

Answers

Answer:

True

Step-by-step explanation:

It's true becuase you need to make each side of the equation equalivant.

Answer:

False

Step-by-step explanation:

Have a wonderful day !!!

What properties do all parallelograms possess?

Answers

Opposite sides are parallel.
Opposite sides are congruent.
Opposite angles are congruent.
Consecutive angles are supplementary.
The diagonals bisect each other.

PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!

PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS

Answers

Answer:

pi, and square root of 2

I don't think you're ACTUALLY going to give me brainliest

Please HELP me ASAP... Don't answer if you don't know all of the questions

Please HELP me ASAP... Don't answer if you don't know all of the questions
Please HELP me ASAP... Don't answer if you don't know all of the questions
Please HELP me ASAP... Don't answer if you don't know all of the questions
Please HELP me ASAP... Don't answer if you don't know all of the questions

Answers

False b/c the line doesn't perfectly bisect two of the sides.Adjacent because they share a sideParallel since they share the same planeRight triangle since two of the interior angles are complementary

The cross section of a parabolic reflector has a vertical axis of symmetry with its vertex at (0,0). The focus of the reflector is 6 feet above the vertex. The reflector extends 5.5 feet to either side of the vertex. What is the depth of the reflector? Round your answer to the nearest hundredth.


The depth of the reflector is about _____

feet.

Answers

Answer:

1.26 feets

Step-by-step explanation:

Given the following :

Vertex (0, 0)

Focus of reflector = 6 feets

Extension = 5.5 feets

Equation to obtain conic section of a parabola:

(x - h)² = 4p(y - k)

Vertex (0, 0)

h =0 ; k = 0, p = 6, x = 5.5

(5.5 - 0)² = 4*6(y - 0)

30.25 - 0 = 24(y - 0)

30.25 = 24y

y = 30.25 / 24

y = 1.26

Hence, depth of reflector = 1.26 feets

Use multiplication properties to find the product. 3 x (3 x 7) =

Answers

The given expression is

3(3 * 7)

The multiplication properties include

1) Commutative property: When two numbers are multiplied together, the product is the same regardless of the order of the multiplicands.

This means that

3 * 7 = 7 * 3 = 21

3 * 21 = 63

2) associative property.: when 3 or more numbers are multiplied, the product is the same regardless of the grouping of the factors. This means that

3(3*7) = 7(3 * 3) = 3(7 * 3) = 63

4.Cost of 10 book is ₹800.What is the cost of 50 such books

Answers

Answer:

₹4000

Step-by-step explanation:

₹800/10 books

₹80/1 book

(₹80/1 book)*(50) = ₹4000

Please answer this question.

Please answer this question.
Please answer this question.

Answers

Sequence A? Sorry if this is wrong!! Good luck!!

what percentage of the variation in productivity is explained by the quadratic regression model?

Answers

Depends on the specific data and coefficients of the quadratic regression model used.

The coefficient of determination, denoted as R-squared (R2), is used to calculate the percentage of variation in productivity explained by the quadratic regression model. R-squared is a statistical measure that represents the proportion of the variance explained by an independent variable or variables in a regression model for a dependent variable.

R-squared is calculated by comparing the total sum of squares (TSS) and the residual sum of squares (RSS):

TSS = Σ(y - ȳ)^2

RSS = (y - - x - b*x2)2.

where y is the actual productivity value, is the mean of the productivity values, x is the independent variable, and b are the quadratic regression model coefficients.

R-squared can be calculated using the formula:

R2 = 1 minus (RSS/TSS)

We can then convert R-squared to a percentage to get the percentage of variation in productivity explained by the quadratic regression model.

As a result, the answer to this question is dependent on the specific data and quadratic regression model coefficients used.

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The instructions for a fashion design project require three different cuts of silk The
longest piece must be twice the length of the middle-sized piece, and the shortest
piece must be ten inches shorter than the middle sized piece. The total length of the
piece of silk you are given to work with is 70 inches. How long should each of the
three cut pieces be?

Answers

The three cut pieces should be 10 inches, 20 inches, and 40 inches  for the shortest, middle-sized and longest respectively

How to determine how long should each of the three cut pieces be?

This is a word problem. We need to understand the sentence in order to translate it correctly.

To find the length of each of the three cut pieces, we can use the given information to set up a system of equations.

Let L, M and S be the length of the longest, middle-sized and shortest piece respectively

So we can set up the following equation:

L = 2M

S = M-10

L + M + S = 70

2M + M + (M - 10) +  = 70

We can combine like terms to get:

4M - 10 = 70

4M = 80

We can divide both sides by 4 to get:

M = 20

Therefore, the length of the middle-sized piece is 20 inches.

Since L = 2M

L =  2 × 20 inches = 40 inches.

Since S = M - 10

S = 20 - 10 = 10 inches.

Therefore, the three cut pieces should be 10 inches, 20 inches, and 40 inches for the shortest, middle-sized and longest respectively

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1.a) In each case either show that G is a group with the given operation or list the axioms that fail.(a) G = N; addition(b) G = R; a · b = a + b + 1(c) G = {16, 12, 8, 4}; multiplication in Z20

Answers

(a) G = N; addition

To show that G = N (the set of natural numbers) under addition is a group, we need to verify the four group axioms:

Closure: For any a, b in N, a + b is also in N.

Associativity: For any a, b, c in N, (a + b) + c = a + (b + c).

Identity element: There exists an element 0 in N such that for any a in N, a + 0 = a.

Inverse element: For any a in N, there exists an element -a in N such that a + (-a) = 0.

Closure and associativity hold for addition on N, so we only need to verify the identity and inverse elements.

Identity element: The only possible identity element is 0, since adding any natural number to 0 gives that number. Thus, 0 is the identity element of (N, +).

Inverse element: For any a in N, there is no element -a in N such that a + (-a) = 0. Therefore, G = N under addition is not a group, because the inverse element axiom fails.

(b) G = R; a · b = a + b + 1

To show that G = R (the set of real numbers) under the given operation is a group, we need to verify the four group axioms:

Closure: For any a, b in R, a + b + 1 is also in R.

Associativity: For any a, b, c in R, (a + b + 1) + c = a + (b + c) + 1.

Identity element: There exists an element e in R such that for any a in R, a + e + 1 = a. Solving for e, we get e = -1, so -1 is the identity element of (R, ·).

Inverse element: For any a in R, there exists an element b in R such that a · b = e. Solving for b, we get b = -a - 2. Thus, for any a in R, -a - 2 is the inverse element of a.

Therefore, G = R under the given operation is a group.

(c) G = {16, 12, 8, 4}; multiplication in Z20

To show that G under multiplication modulo 20 is a group, we need to verify the four group axioms:

Closure: For any a, b in G, ab mod 20 is also in G.

Associativity: For any a, b, c in G, (ab)c mod 20 = a(bc) mod 20.

Learn more about closure here : brainly.com/question/19340450

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